goals: define a polygon define and use reflectional symmetry and rotational symmetry

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Goals: • Define a Polygon • Define and Use reflectional symmetry and rotational symmetry • Define regular polygon and use the central angle theorem of a regular polygon POLYGONS AND SYMMETRY

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Polygons and Symmetry. Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry Define regular polygon and use the central angle theorem of a regular polygon. Examples. Not Polygons. Polygons. Vocab. - PowerPoint PPT Presentation

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Page 1: Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry

Goals:•Define a Polygon

•Define and Use reflectional symmetry and rotational symmetry

•Define regular polygon and use the central angle theorem of a regular polygon

POLYGONS AND SYMMETRY

Page 2: Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry

EXAMPLES

Polygons Not Polygons

Page 3: Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry

VOCABTerm Picture Definition

Polygon

Sides of a Polygon

Vertices of a Polygon

Segments of a polygon

A closed plane figure formed by three or more segments such that each intersect exactly two other segments.

The common endpoints of those segments

Page 4: Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry

Term Picture Definition

Equiangular Polygon

Equilateral Polygon

Regular Polygon

Central Angle

All angles congruent

All sides are congruent

Both equiangular and equilateral

An angle whose vertex is the center of the polygon and whose sides pass through two consecutive vertices

Page 5: Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry

POLYGONS CLASSIFIED BY NUMBER OF SIDES

# sides Name of Polygon

# sides Name of Polygon

3 triangle 9 nonagon

4 quadrilateral 10 decagon

5 pentagon 11 11-gon or hendecagon

6 hexagon 12 dodecagon

7 heptagon 13 13-gon

8 octagon n n-gon

Page 6: Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry

Reflectional Symmetry: A figure has reflectional symmetry if and only if

its reflected image across a line coincides exactly with the preimage, the original figure.

Axis of Symmetry: A line that divides a figure into two congruent reflected halves.

Page 7: Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry

DRAW ALL AXES OF SYMMETRY ON EACH FIGURE

Page 8: Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry

Rotational Symmetry: A figure has rotational symmetry if and only

if it has at least one rotation image not counting rotation images of 0º or multiples of 360º, that coincide with the original figure.

Page 9: Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry

HOW MANY TIMES DOES EACH FIGURE HAVE ROTATIONAL SYMMETRY?

Page 10: Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry

ACTIVITY WITH PATTY PAPER…

The measure of a central angle of a regular polygon with n sides is given by the following formula:

___________________________

Page 11: Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry

EXAMPLE 1: FIND THE MEASURE OF THE CENTRAL ANGLE OF EACH REGULAR POLYGON BELOW:

a) decagon b) heptagon c) 15-gon

Measure of central angle: Measure of central angle: Measure of central angle:

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